Zimmer told reporters on Sunday that Elflein will not return to practice this week ahead of the team's final preseason game on Thursday. The second-year player was placed on the preseason physically unable to perform list on July 25.
Hours after Zimmer updated reporters on Elflein's condition, the Vikings acquired center Brett Jones from the New York Giants.
The Vikings sent a 2019 pick to New York for Jones, who appeared in 30 games for New York. He does have 12 starts at center.
Elflein underwent two surgeries in the offseason after fracturing his left ankle in the NFC Championship Game against the Philadelphia Eagles. He also injured his shoulder in Atlanta in December.
The 24-year-old has been limited to working out with trainers in the weight room and on a rehab field over the last month.
"He's going to practice when he's ready to go," Zimmer said, per ESPN. "I don't know when that's going to be."
A third-round pick in the 2017 NFL Draft out of Ohio State, Elflein started 14 regular-season games and two postseason contests for the NFC North champion Vikings. He helped the club's rushing offense finish seventh overall in the league, one season removed from ranking 32nd overall.
Elflein missed two games in the final stretch of the season with a shoulder injury.
The Vikings lost left guard Nick Easton for the season after he underwent surgery to repair a bulging disc in his neck while right guard Mike Remmers just returned from an injured ankle.